Advertisements
Advertisements
Question
Find the following integrals:
`int(1 - x) sqrtx dx`
Advertisements
Solution
`int (1 - x) sqrtx dx`
`I = int (x^(1/2) - x^(3/2))` dx
`I= int x^(1/2) dx - int x^(3/2)` dx
`I= 2/3 x^(3/2) - 2/5 x^(5/2) + C`
APPEARS IN
RELATED QUESTIONS
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int(2x^2 + e^x)dx`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`1/((x^2 + 1)(x^2 + 4))`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal
`int (dx)/sqrt(9x - 4x^2)` equal
`int (dx)/sqrt(9x - 4x^2)` equals
`int (xdx)/((x - 1)(x - 2))` equals
`int sqrt(1 + x^2) dx` is equal to
If the normal to the curve y(x) = `int_0^x(2t^2 - 15t + 10)dt` at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
In \[\int f(x)\,dx\], what is \(f(x)\) called?
In \[\int f(x)\,dx\], what is \(x\) called?
What is \(C\) called in \[\int f(x)\,dx=F(x)+C\]?
Evaluate \[\int \sin x\,dx\]
Evaluate \[\int \text{cosec}^2 x\,dx\]
Evaluate \[\int \sec x\tan x\,dx\]
Evaluate \[\int \frac{dx}{1+x^2}\]
